Why is voltage subtracted in this 2-resistor circuit to find the current?

Question

I am figuring out the current for the following circuit:

Using V = IR, I would expect to do I = V / R and then do:

I = (20 + 50) / (1 + 2) = 70 / 3 Amps.

However, the actual current is:

(20 - 50) / 3 = -10 Amps

Why are the voltages subtracted rather than added?

References to blog posts / textbook chapters would also be appreciated (if available).

Here's the full solution, if it helps anyone:

@Andyaka, I'm not sure. I guess it isn't specified? I'm using Schaum's Outline of Electric Circuits, so maybe there's some convention in that textbook. — Foobar, Commented Sep 16, 2021 at 17:09
@Andyaka, I've added the full solution to the post -- if that gives additional context. — Foobar, Commented Sep 16, 2021 at 17:11
The voltages are added. However, in going round the loop in a consistent direction, one voltage has the opposite polarity to the other. What's (+50) + (-20)? — Neil_UK, Commented Sep 16, 2021 at 17:13
@Andyaka, ok I think I've figured it out. The voltages are series opposing since the (+) signs are facing each other. 50 - 20 = 30 V. V = I / R = 30 / 3 = 10. However, the sign is negative since it's asking us to find the current flowing clockwise, but in reality the current is flowing counter-clockwise. — Foobar, Commented Sep 16, 2021 at 17:18

G36 · Accepted Answer · 2021-09-16 17:35:46Z

1

Try to analyze this equivalent circuit

schematic

^{simulate this circuit – Schematic created using CircuitLab}

As you can see from node A to B we have a voltage rise by 20V and from B to node C we have a voltage drop by 50V. Therefore V_CA = +20 - 50V = - 30V.

answered Sep 16, 2021 at 17:25

G36

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